President Trump, in a combative news conference on Monday, falsely and repeatedly asserted that he had the unilateral power to compel states to lift stay-at-home orders and businesses to open. Here’s a fact check of that and other claims.

What Was Said

Reporter: “There’s a debate over what authority you have to order the country reopened. What authority do you have on this one?”
Mr. Trump: “Well, I have the ultimate authority.”

False. He does not have the authority to override stay-at-home or shelter-in-place orders from governors, or “total” authority in general.

“I don’t know of anything that would allow him to do this,” said Chris Edelson, a professor of government at American University. “We live in a constitutional system with checks and balances. Nobody has total authority.”

“The President has no formal legal authority to categorically override local or state shelter-in-place orders or to reopen schools and small businesses,” Stephen I. Vladeck, a professor at the University of Texas School of Law, said on Twitter. “No statute delegates to him such power; no constitutional provision invests him with such authority.”

At his news briefing, Mr. Trump repeated his position a number of times.

“The president of the United States calls the shots,” he said. “They can’t do anything without the approval of the president of the United States.”

Asked what provisions of the Constitution gave him such authority over the states, he replied, “Numerous provisions,” without naming any. “When somebody’s the president of the United States, the authority is total.”

Even the emergency powers granted to the federal government come with limits and “none of these authorities says the president can do anything that he wants,” said Elizabeth Goitein, who directs the Brennan Center for Justice’s Liberty & National Security Program.

“The framers of the Constitution did not come up with a system” without limits on executive power, she added. “They were kind of trying to do the opposite of that.”

While the federal government has authority over interstate and foreign quarantine measures, states have the primary authority to impose and enforce quarantine and isolation measures within their own borders, as part of the police powers conferred to states by the 10th Amendment of the Constitution, according to the Congressional Research Service and the Centers for Disease Control and Prevention.

The Federal Emergency Management Agency, in batting down untrue rumors on its website, noted that “states and cities are responsible for announcing curfews, shelters in place, or other restrictions and safety measures.” Mr. Trump’s claims were also contradicted by Gov. Larry Hogan of Maryland and Gov. Chris Sununu of New Hampshire, both Republicans, who said on Monday that the decision to lift measures was up to the states.

“Just last week, we were asking: Why no national lockdown? The answer is that state governors are responsible for the health of their populations, as Trump himself has said,” said Polly J. Price, a professor of global health and law at Emory University. “Is Trump’s next step to nationalize the manicure industry? Because unless he is going to nationalize specific businesses, like wartime industry, this is a state matter.”

Even in a hypothetical scenario, Mr. Trump would be limited in how he can act. Congress could conceivably pass a law on interstate commerce that would effectively compel states to rescind their stay-at-home orders, but the president could not unilaterally act to do so. Similarly, while it’s possible that classified draft documents or the Justice Department’s Office of Legal Counsel have argued for an expansion of executive power including authority to override governors, such powers have yet to be invoked and could still be challenged in court.

Though Mr. Trump said he could provide “a legal brief” on “numerous provisions” in the Constitution that outline his authority to override governors, the White House did not respond when asked for the brief or other evidence of the president’s claims.

What Was Said

“Nobody is asking for ventilators.”

False. Several governors continued to speak about existing or impending shortages of ventilators and other supplies.

“Everybody still has tremendous needs on personal protective equipment and ventilators and all of these things that you keep hearing about. Everybody’s fighting to find these things all over the — all over the nation and all over the world,” Mr. Hogan said on ABC’s “This Week” on Sunday.

“The White House, over the past number of weeks, has delivered a series of tranches of ventilators and other personal protective equipment. But we continue to be shy on all — all fronts,” Gov. Phil Murphy of New Jersey said that same day on CBS.

What Was Said

“When on January 31, I instituted the ban, Joe Biden went crazy. He said you don’t need the ban … He called me xenophobic. He called me a racist, because he has since apologized and he said I did the right thing.”

This is exaggerated. Mr. Biden, the presumptive Democratic nominee, has generally criticized Mr. Trump for “xenophobia” and “fear-mongering” in his response to the coronavirus. But The Times was unable to find an instance of him using those words to describe the restrictions Mr. Trump imposed on travel from China in January. Mr. Trump later used the phrase “Chinese virus” in describing the outbreak.

In April, the Biden campaign said that Mr. Biden supported the restrictions, as they had the backing of scientists and public health officials. There is no public record of an apology to Mr. Trump.

What was said

“The United States has conducted three million tests for the virus, three million, the most of any nation.”

This is misleading. Mr. Trump’s figures were in line with estimates from the COVID Tracking Project, which reported about 2.9 million tests, or about 883 tests per 100,000 people, as of Monday night. That is the most in the world in raw numbers, but the United States still lags behind other countries in testing per capita. In comparison, South Korea has conducted 958 tests per 100,000 and Italy more than 1,700 tests per 100,000.

The president noted this distinction moments later when he touted New York’s testing figures in per capita terms.

Curious about the accuracy of a claim? Email factcheck@nytimes.com.